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PLAN OF 1 RELATIVISTIC_PHENOMENOLOGY
1a introduction
1b information processing
1c mind and brain
1d mapping and modeling
1e causality or implication
BACK TO SITE PLAN
1E CAUSALITY AND IMPLICATION
1Ea Introductory Quotation
NOTE: neologies and ambiguous terms clarified in GLOSSARY
are marked "[G]".
Let's start by a quotation of Charles Sanders Peirce
(Reasoning and the Logic of Things):
"Those who make causality one of the original uralt elements
in the universe or one of the fundamental categories of
thought - of whom you will find that I am not one - have one
very awkward fact to explain away. It is that men's
conceptions of a cause are in different stages of scientific
culture entirely different and inconsistent. The great
principle of causation which, we are told, it is absolutely
impossible not to believe, has been one proposition at one
period in history and an entirely disparate one at another
is still a third one for the modern physicist. The only thing
about it which has stood... is the name of it."
Structure and Faculties of Mind
In BAA.STRUCTURE OF MIND we established the structure of
Mind encompassing three basic Referentials: Sensorium,
Imagery and Symbolics. This static structure is processed
by several dynamic Functions or Faculties of human
"Reason":
-Morphogenesis, processing the Association Sensorium/Imagery.
-Imagination, processing Imagery.
-Logic, processing Symbolics.
-Reflection, processing the Association Imagery/Symbolics.
Reflection, sometimes called Lateral Thinking, consists of
two basic faculties:
1.Symbolizing, or mapping Imagery to Symbolics.
2.Understanding, or reducing Symbolics to Imagery.
We Symbolize by mapping Images of Imagery into Inference or
ER (Entity/Relation) networks of Symbolics, following
respectively Causality and Encompassing Orders. Symbolic
networks may be expressed with Statements and Symbols of our
languages. (Details in REFLECTION SPIRAL).
We Understand ER network structures as well as linguistic
Statements and Symbols by imagining them, by reducing them
to Imagery, which confers on them signification and meaning.
Symbolizing and Understanding are synonyms of covariant
reciprocal transformations between Imagery and Symbolics.
As we said above, a particular Orderer of Imagery is the
Causality Relation, which, by virtue of Reflection, transfers
into Symbolics as Logic and its Inference faculty.
E-Locality and Causality
Extended Locality (E-Locality), Definition:
Two PS Events are said to be "E-locally related" (in a Model)
when their Model's AS representations are continuously
Transportable via a geodesic of Field/#Space[G] Continuum to
the same "location" or point of this Continuum. E-Locality
is clearly Model dependent.
This "Extended Locality" clarifies the common, confusion of
"locality" with a single point of #Space: a #Space point
represents a single Event and no other Event can refer to it.
By virtue of the Extended Locality even such distant bodies
as Earth and Moon are locally related via the Gravity Field
Continuum. We shall further understand the term 'Locality'
as synonym of 'E-Locality', unless differently defined, in
which case we shall mark it with inverted commas, as
"locality".
Given E-locally related Events A,B we shall say that they
appear respectively as "Cause" and "Effect" if B has never
been observed without A, while A might have been observed
without B.
Thus force appears as Cause of acceleration as the latter
has never been observed without the former, while force
is often observed without acceleration.
Causality Relation transforms into Implication Relation of
Model's Abstract #Space. Thus, we consider Causality as
P-Equivalent with Implication: to say "A is cause of B" is
for us equivalent with "A implies B".
Weak verifiability and strong falsifiability of Implication
(see below) embodies the uncertainty of Causality which is
hypothetical, never verified, but at best not (yet)
falsified by eventual observation of Effect lacking its
apparent Cause. Taking into account the fundamental
fuzzyness of Observations ( INTRODUCTION TO RELATIVISTIC PHENOMENOLOGY
we can conclude:
CAUSALITY IS HYPOTHETICAL, FALSIFIABLE AND FUZZY.
As a necessary foundation of implicative cognitive and
scientific Models it extends over them these qualities.
Effectivity and Finality
Events extending over perception and introspection,
span past history and future projects, so that Causes
may be past, aka. Effective or future, aka. Final.
Both Effectivity and Finality are P-Equivalent[G] with
Implication.
Effectivity controls factual inquiry and evidence.
Finality controls human projects, including concepts
of scientific Models, their predictions and plans of
their experiments.
Encompassment
In BAA.STRUCTURE OF MIND we have seen
that Imagery basins may encompass one another or be related
by Encompassment Relation. Encompassment is a particular
case of Causality and likewise transformsto Implication:
-Encompassing Entity, the more general "Aggregate" or
"Class" implies the encompassed, more particular "Part"
or "Instance".
-By virtue of the Extended Locality, Aggregate or Class is
locally related to Part or Instance.
-Thus, Encompassment map to logical Implication structure
is equivalent to that of Causality.
To resume:
-IMPLYING Cause, Aggregate or Class is a deductive
Presumption,
-IMPLIED Effect, Part or Instance is its inductive
justification.
And more briefly:
-Cause implies Effect.
-Effect justifies Cause.
EA. LOGICAL ASPECTS OF IMPLICATION
For compatibility with Fuzzy Logic
(CCA.COGNITIVE NETWORK)
we shall call the Boolean variable "Certainty". Replacing
binary Certainty values 1/0 with "true/false", the logical
construct "A implies B" admits 4 cases:
Certainty of: A B Implication
1. true true true
2. true false false
3. false true true
4. false false true
Let A and B denote for illustration purpose:
A = "it rains" (shortly "rain")
B = "street is wet" (shortly "wet_street").
Implication, has two aspects
-Deductive top-down "rain implies wet_street", where "rain"
and "wet street" are assertions and Implication represents
a simple deductive "Theory".
-Inductive bottom-up verification elevating the Theory to an
empirically verifiable "Model". Certainty of inductive
bottom premises ("rain", "wet_street") is "factual", set by
observations and spread inductively over the structure (in
our example the structure is reduced to one Implication).
The great difficulty of scientific Models consists in the
"true" cases 1,3,4 being unable to affirm that the Model is
right, only that it is not (yet) false. "True" value of
Implication confers on the Model the benefit of doubt. The
case 3., for instance, says that the street was wetted by
something else than rain, say by firemen, which does not
affirm anything about rain wetting the street, or otherwise.
Even the case 1. which verifies the predictions, cannot
affirm that the Model is well founded. Indeed, some streets
may be sheltered from rain, or some particularly strong
khamsin may dry the street before it gets wet, so that in
spite of rain, the wetness may be due to firemen. Still,
persistent repetitions of case 1. may bring forth the belief
in the essential accuracy of the Model. But it will be no
more than a probability based belief.
Only case 2. would affirm something sure about Implication,
namely that it's false.
We may say that Implication has weak verifiability and
strong falsifiability.
Field Models
There are currently two universally acknowledged Field
Models: Extended Relativity (including the Special and the
General) and QFT (Quantum Field Theory). They are both
founded in Field seen as Dialectic Phenomenon embracing the
Aspects of Continuum and Discrete Singularities called
"matter" or "particles". Within this basic structure the
difference is restricted to the focus of interest:
Relativity concentrates on Field Continuum and its
P-Equivalence with #Space,
-QFT - on Field Singularities or "particles".
Relativity
Relativity dismisses all knowledge of Singularity internals,
beyond the Event Horizon. On the other hand, in apparent
contradiction, its fundamental axiom of Field speed C being
independent of the speed of Field source and observer clearly
implies Singularities as Field emitters and receptors.
Strictly speaking, Field sources and sinks are Mathematical
Singularities, i.e. points at which Field's magnitude
increases or decreases, points at which Field originates or
vanishes. They are mathematically expressed by the Vector
Analysis operator "Divergence", positive for source and
negative for sink. These sources and sinks are strictly
speaking the unique conceivable poles of "action". Yet, they
are incognizable, being the details of physical Singularities
located beyond the Event Horizon.
Fortunately it does not mean that the problem of Locality is
unsolvable. Indeed, even intuitively we see that Singularities,
the "black matter holes" are homomorphic with the Continuum
and "black" only due to the limitations of our physical and
mathematical tools. This intuition is rigorously confirmed
by Mathematics: the Ostrogradsky Theorem allows to express
the global Divergence of a bounded volume (volume integral
of Field Divergence) as Field Flux across the bounding
surface (surface integral of Field). Thus, while ignoring
the details of a Singularity, we can rigorously evaluate its
global "action" in terms of the cognizable Continuous Field
Flux across its boundary. In other terms, Discrete "action"
is reduced to Continuity. Singularities may act on one another,
i.e. exchange Information only via Field Continuum.
This reduction reaffirms the well known principles of
Relativity:
-Field "action" is Local,
-Distant "action" occurs exclusively as propagation of local
information impulses along continuous trajectories of #Space
(P_Equivalent of Field),
-"Action", i.e. Information moves across #Space at speed
never exceeding C.
Quantum Field Theory (QFT)
QFT accepts the fundamental relativistic context of Field
P_Equivalent to #Space, embracing two Aspects, the Continuum
and Discrete Singularities thereof, called "matter" or
"particles". Consequently, from the point of view of Locality
it reiterates the relativistic principles of Local "action",
of local information impulses propagating along continuous
paths and of information moving at speed never exceeding C.
Thus, differences between Relativity and QFT don't concern
the Field/Singularity context, but their foci of interest,
respectively Field Continuum and Field Singularities.
Locality principle is accepted and supported by both. It's
true that QFT has some fundamental problems, but they are
of mathematical nature, due to lacking tools to deal with
Singularities and have no impact on Locality.
(As Dirac said: "There must be some fundamental change in
our ideas, probably a change just as fundamental as the
passage from Bohr's orbit theory to quantum mechanics.
When you get a number turning out to be infinite which ought
to be finite, you should admit that there is something wrong
with your equations, and not hope that you can get a good
theory just by doctoring up that number.")
Quantum Theory (QT)
Phenomenal sense of physical Models stems from the interplay
of Continuum and Discreteness, P_Equivalent complementary
Aspects of Universe
(INTRODUCTION TO RELATIVISTIC PHENOMENOLOGY
QT dismisses the Continua of Field and #Space and deals
exclusively with Discrete "matter corpuscles". Thus, it is
a recipe of formulas void of Phenomenal sense.
Feynman said it in different terms:
**I think I can safely say that nobody understands
Quantum Mechanics**.
In particular, Quantum Entanglement, pretending that
measurements performed on spatially distant parts of
a quantum system affect one another simultaneously, is
entirely senseless, as in lack of defined #Space, the
concepts of distance and simultaneity are undefined and
hollow.
The same concerns pretended information propagation or
"teleportation" at speeds exceeding C, which, in absence
of defined #Space, is neither true nor false, but simply
void of sense.
Some essential concepts of QT such as the Wave Function,
its collapse and the Double Slit experiment are discussed
in APPENDIX.
Newton Model
Newton, the probably greatest scientist was paradoxically
the most paradoxical. We discuss his Model and its
paradoxes in some detail in
0B GALILEAN RELATIVITY AND NEWTON'S MODEL .
EC. RECIPROCITY
Traditional Noumenalistic Logic and Causality were unable
to define, let alone to solve the problem of Reciprocity
involved by such fundamental constructs as Newton's
Action / Reaction or Continuum / Discreteness of Field and
its "matter" Singularities. Some views consider discrete
"matter" as cause of the Continuous Field generated by
deployment of Singularities. Other ones see Discreteness as
effect of Continuum culminating in Singularity areas.
It's a clear vicious circle, just like that of Acting Force
causing Reacting Force which in turn causes the Acting Force.
In terms of our Phenomenology, Reciprocity is not a "causal",
logical Implication, but a juxtaposition of P-Equivalent
Aspects of Phenomenal Dialectic structure.
They don't "cause" or imply one another, but are both implied
by their founding Phenomenon. Two opposed Forces are
P-Equivalent aspects of the Phenomenon "Action".
Continuous areas and Discrete Singularities are P-Equivalent
aspects of the Phenomenon "Field".
Expressions
We have discussed so far the "lower" inductive premises
globally without considering their internal structure.
Yet, as all symbolic Entities, they are maps of Imagery
Patterns composed in general of several Basins. We shall
say that a Pattern maps into an composite Entity or a
structure of interrelated Entities, which we shall call
"Expression". Within an Expression, Entities are related
by "Logical Operators", such as AND, OR, OOF (One Of), etc.
Details are discussed in CCA.COGNITIVE NETWORK
and in not yet uploaded chapter on the ER Theory, replacing
the current ill founded Set Theory.
Most generally, we can see our logical "Cognitive Network"
as a structure of horizontal Expressions related vertically
by Implications.
We saw in the paragraph "Encompassment" above, that
Encompassment's logical maps are equivalent with those
of Causality. Consequently, the Cognitive Network supports
equally well the traditional logical problems, as the ER
(Entity-Relation) Theory, the Phenomenological counterpart
of the naive noumenal Set Theory.
We have seen above ("Locality and Causality") that
CAUSALITY IS HYPOTHETICAL, FALSIFIABLE AND FUZZY.
As the ontological foundation of Cognitive Network, it
extends these qualities over its all applicative instances.
Appendix
(In editing)
